The short answer is “yes they can have access to that data”.I wonder if they also (can) have access to airline companies data. With that it would be piece of cake to assess whether someone has been 180+ day somewhere or not. After all, once IG and FB will be known issue, non-idiots will stop using them
In Schengen, if you are from a country that subscribes to Schengen, you won’t get an entry / exit stamp. If you are from outside Schengen you get an entry stamp in the entry country and an exit stamp in the exit country. In the mean time you can travel in the Schengen area if your visa allows it.If I am not wrong, Just checking your passport , Police can find where you live ?
Every country you visit has entry and exist stamp.